"Check for updates" should offer the updates for installation if available
Binary package hint: update-notifier
The right-mouse menu of the update-notifier applet has the following options:
Show updates - does the same thing as left-clicking (do we need two ways to do this?)
Install all updates - installs updates already known to be available
Check for updates - checks for new updates, then exits (see below)
Start package manager - run Synaptic interactively
I think "Check for updates" should, after checking for updates, display the available updates to the user in the same manner as "Show updates" or left-clicking. If the user is asking to check for updates immediately, they are clearly interested in what is available and probably want to install it. As such, I think it's appropriate to interact with them if there are updates available (which is always true, because otherwise the icon is hidden).